I have a Technics SU-800 50x50w amp, and a pair of floorstanding 90w speakers. I have a passive subwoofer that I have just built. The amp has two sets of speaker terminals, A and B. I am aware that it is just two amps for both A and B, but I would like to have the sub running centrally.
I've seen articles online which say to connect it to the positive terminal on one channel and the negative on the other, but I'm worried it'll kill the amp or at least damage it.

I would have thought that the two sets of speakers A & B would be wired in series and driven by the one internal amplifier. What you are attempting to do is to have a mono feed to the sub, which IMO you cannot do with this amp configuration. You cannot simply bridge the channels in this way (AFAIAA)

Will it kill your amp? If you run the sub in conjunction with your main speakers (say from set B) there will probably be a warning on the back of the amp telling you not to use 2 sets of speakers that are less that 8 Ohms.

Connecting the sub in the way you describe, is the same as connecting it to one channel only, because the negative terminals of both channels are ground.

What you have seen is a solution for car amps that are designed for bridged as well as stereo operation. In that case the signal of one channel is inverted and both channels work in BTL mode on the woofer.

It is possible to build a passive crossover that mixes the sub-signal to a mono signal for the sub. Due to the low crossing frequency the necessary components for such a crossover are easily as expensive as a plate amp with built-in active crossover, so it is certainly better to go that route. Especially as you need to adjust the crossover frequency, phase and volume to match your mains speakers which you can easily do on a plate amp with no additional cost, but not so in a passive crossover.